Analysis on sampling bounds for digital spectrometers

In this paper, the impact of random arrival time on the amplitude resolution is analyzed for digital spectrometers. The improvement performance of amplitude estimation is also analyzed by using timing techniques. This effect relies on the sampling frequency f
s
and the characteristics of analog section and digital filters. The equivalent noise charge ENC
a
and baseline V
BL
caused by this effect is derived for digital filters. For the digital trapezoidal filter using a charge sensitive preamplifier and a simple CR-RC circuit as analog section, the minimum f
s
is required to be 7/τ to make ENC
a
/ Q
in
lower than 10−
³
, i.e. ENC
a
is only 6.25 electrons with 1 fC detector charge. The Cramer-Rao Limited Bounds (CRLB) for estimating arrival time and amplitude synchronously is also calculated. This work will provide a selection criterion for choosing f
s
, analog prefilter and timing method to reduce the influence of random arrival time.